A Seamless Startup and Phase-Locked Control Strategy for High-Q Hemispherical Resonator Gyroscopes based on Nonlinear Self-Excitation

The high quality factor of Hemispherical Resonator Gyroscopes (HRGs) significantly reduces thermoelastic noise but introduces severe challenges for closed-loop startup. Due to the extremely narrow bandwidth, traditional Phase-Locked Loop (PLL) with linear frequency sweeping suffers from the chirp effect, leading to prolonged energy accumulation times or complete capture failures. To address this bottleneck, this paper proposes a rapid startup and robust synchronization control strategy based on nonlinear self-excitation. First, a phase-compensated hard-limiter feedback loop is designed to spontaneously lock onto the mechanical resonance, maximizing energy injection and entirely eliminating the frequency-searching overhead. Second, to prevent transient mechanical shocks during the transition to steady-state operation, a discrete-time bumpless mode-switching logic is formulated. By implementing a dual-criteria evaluation comprising amplitude thresholds and background phase pre-synchronization, the system achieves a mathematically continuous handover to a linear Digital PLL (DPLL) with Automatic Gain Control (AGC). The proposed architecture effectively decouples the startup speed from the steady-state precision, offering a highly robust digital control solution for high-performance vibratory gyroscopes.